The deep insight: A tensor is not a grid of numbers. A tensor is a geometric object living on a manifold. Coordinates are just temporary scaffolding.

It sounds like you're looking for a about Tensor Calculus by J.L. Synge and A. Schild — likely to share on a forum, social media, or study group.

If you’ve struggled with other tensor books, try this. Read it slowly. Draw pictures. Ignore the 1940s notation quirks. Beneath the age is a clarity that modern texts often miss.

Most introductions to tensor calculus drown you in indices by page 3. But Synge & Schild do something different.